On the special identities of Gelfand--Dorfman algebras
In this paper, we prove that the class of all special Gelfand--Dorfman algebras (GD-algebras) is closed with respect to homomorphisms and thus forms a variety. We also prove that every 2-dimensional GD-algebra is special. For the latter, we give a technical method to find all special identities of G...
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description | In this paper, we prove that the class of all special Gelfand--Dorfman algebras (GD-algebras) is closed with respect to homomorphisms and thus forms a variety. We also prove that every 2-dimensional GD-algebra is special. For the latter, we give a technical method to find all special identities of GD-algebras and compute the degree 6 component of the Gr\"obner basis for the shuffle operad constructed on the symmetric operad governing the class of GD-algebras. |
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title | On the special identities of Gelfand--Dorfman algebras |
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